Question

In a study about undergraduate student credit card usage, it was reported that undergraduate students have a mean credit card balance of $3173 (Sallie Mae, April 2009). This figure was an all-time high and had increased 44% over the previous five years. Assume that a current study is being conducted to determine if it can be concluded that the mean credit card balance for undergraduate students has continued to increase compared to the April 2009 report. Based on previous studies, assume a population standard deviation of 1350. Suppose you look at a random sample of 192 undergraduate students with a sample mean credit card balance of $3426.3. You wish to test the claim that the mean credit card balance is higher than it was in 2009 at the α = 0.002 level.

Answer 1

given data are:-

sample mean () = 3426.3

population sd () = 1350

sample size (n) = 192

here, as the population sd is known and n >30, we will do 1 sample Z test for mean.

hypothesis:-

test statistic be:-

p value be:-

[ from standrad normal table]

decision:-

p value = 0.0047 >0.002 (alpha)

so, we fail to reject the null hypothesis.

conclusion:-

there is not sufficient evidence to support the claim that the mean credit card balance is higher than it was in 2009 at the α = 0.002 level.

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